For a ferromagnetic material the
$\mu$ and H are related as: $\mu=[\frac{0.4}{H}+12 imes10^{-4}]$ henry/meter.
For B to be 1 tesla, the value of H should be

Question

For a ferromagnetic material the 
$\mu$ and H are related as: $\mu=[\frac{0.4}{H}+12	imes10^{-4}]$ henry/meter. 
For B to be 1 tesla, the value of H should be

Accepted Answer

To determine the correct value of $ H $ for which the magnetic flux density $ B $ is 1 tesla, we need to use the relationship between $ B $, $ \mu $, and $ H $. The relationship is given by:

$$ B = \mu \times H $$

We are given that:

$$ \mu = \left[\frac{0.4}{H} + 12 \times 10^{-4}\right] \text{ henry/meter} $$

We need to find the value of $ H $ such that $ B = 1 $ tesla.

Substitute $ \mu $ into the equation for $ B $:

$$ 1 = \left[\frac{0.4}{H} + 12 \times 10^{-4}\right] \times H $$

Simplify the equation:

$$ 1 = 0.4 + 12 \times 10^{-4} \times H $$

$$ 1 = 0.4 + 0.0012 \times H $$

Subtract 0.4 from both sides:

$$ 0.6 = 0.0012 \times H $$

Solve for $ H $:

$$ H = \frac{0.6}{0.0012} $$

$$ H = 500 \, \text{amp/m} $$

Thus, the correct value of $ H $ is 500 amp/m, which corresponds to Option 4.

### Explanation for Other Options:

1. **Option 1: 240 amp/m**
   - If $ H = 240 \, \text{amp/m} $, substituting into the equation:
     $$ \mu = \left[\frac{0.4}{240} + 12 \times 10^{-4}\right] $$
     $$ \mu = \left[0.0016667 + 0.0012\right] $$
     $$ \mu = 0.0028667 \, \text{henry/m} $$
     $$ B = 0.0028667 \times 240 = 0.688 \, \text{tesla} $$
   - This does not satisfy $ B = 1 \, \text{tesla}$.

2. **Option 2: 48 amp/m**
   - If $ H = 48 \, \text{amp/m} $, substituting into the equation:
     $$ \mu = \left[\frac{0.4}{48} + 12 \times 10^{-4}\right] $$
     $$ \mu = \left[0.0083333 + 0.0012\right] $$
     $$ \mu = 0.0095333 \, \text{henry/m} $$
     $$ B = 0.0095333 \times 48 = 0.4576 \, \text{tesla} $$
   - This does not satisfy $ B = 1 \, \text{tesla}$.

3. **Option 3: 124 amp/m**
   - If $ H = 124 \, \text{amp/m} $, substituting into the equation:
     $$ \mu = \left[\frac{0.4}{124} + 12 \times 10^{-4}\right] $$
     $$ \mu = \left[0.0032258 + 0.0012\right] $$
     $$ \mu = 0.0044258 \, \text{henry/m} $$
     $$ B = 0.0044258 \times 124 = 0.5488 \, \text{tesla} $$
   - This does not satisfy $ B = 1 \, \text{tesla}$.

Therefore, Option 4 is the only correct choice that satisfies the condition $ B = 1 \, \text{tesla} $.